Surfaces and Gradients
Surfaces and Gradients
Visualize how gradients relate to surfaces.
The points satisfying for a particular value of form the surface shown. As varies, the surface deforms along the normals defined by the vector field , the gradient of , represented by the arrows.
(x,y,z)
w=f(x,y,z)=u+v+
2
x
2
y
2
z
w
w
∇f=++
∂f
∂x
i
∂f
∂y
j
∂f
∂z
k
f
Due to the complex nature of this Demonstration, there may be a delay between changing the variables and updating the graph.